Q: For the circuit in the figure, determine the energy stored in the coupled inductors at t = 1.5s.
A: 39.4J
Following is my approach on this problem:
1/8 F => -j4Ω
2H => j4Ω
1H => j2Ω
I determine I1 to be the current in the mesh on the primary side going clockwise, I2 to be the current in the mesh on the secondary side going clockwise.
40 = 4I1-j2I2
0 = (2+j2)I2-j2I1
I1 = (1-j)I2
(4-j6)I2 = 40
I2 = 5.547\(\angle56.3^{\circ}\)
I1 = 7.845\(\angle11.3^{\circ}\)
i2 = 5.547cos(2t + \(\56.3^{\circ}\))
i1 = 7.845cos(2t + \(\11.3^{\circ}\))
at t = 1.5s:
i1 = 7.845cos(\(\183.2^{\circ}\)) = -7.833A
i2 = 5.547cos(\(\228.2^{\circ}\)) = -3.697A
w = \(\\frac{1}{2}*2*(-7.833)^{2}+\frac{1}{2}*(-3.697)^{2}+(-3.697)(-7.833)\) = 97.148J
Please tell me where have I got wrong, thanks!
A: 39.4J
Following is my approach on this problem:
1/8 F => -j4Ω
2H => j4Ω
1H => j2Ω
I determine I1 to be the current in the mesh on the primary side going clockwise, I2 to be the current in the mesh on the secondary side going clockwise.
40 = 4I1-j2I2
0 = (2+j2)I2-j2I1
I1 = (1-j)I2
(4-j6)I2 = 40
I2 = 5.547\(\angle56.3^{\circ}\)
I1 = 7.845\(\angle11.3^{\circ}\)
i2 = 5.547cos(2t + \(\56.3^{\circ}\))
i1 = 7.845cos(2t + \(\11.3^{\circ}\))
at t = 1.5s:
i1 = 7.845cos(\(\183.2^{\circ}\)) = -7.833A
i2 = 5.547cos(\(\228.2^{\circ}\)) = -3.697A
w = \(\\frac{1}{2}*2*(-7.833)^{2}+\frac{1}{2}*(-3.697)^{2}+(-3.697)(-7.833)\) = 97.148J
Please tell me where have I got wrong, thanks!
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